To find the volume of the prism, we multiply the length, width, and height together:
Volume = (1/2) * (1/4) * (5/4) = 5/32 cubic meters
Now, to check this volume by packing the prism with 10 unit cubes (each with an edge length of 1/4 meter), we calculate the number of cubes needed to fill the prism:
Number of cubes = (1/2) / (1/4) * (1/4) / (1/4) * (5/4) / (1/4) = 10 cubes
Since we used 10 cubes to fill the prism, the volume calculated by multiplying the edge lengths is correct:
Volume = 10 cubes = 5/32 cubic meters
Therefore, the volume of the prism is 5/32 cubic meters.
Use the image to answer the question.
An illustration shows a 3 D rectangular cuboid segmented into 5 rows by 2 columns of blocks. The length is start fraction 1 over 2 end fraction, width is start fraction 1 over 4 end fraction, and height is start fraction 5 over 4 end fraction.
Multiply the edge lengths of a right rectangular prism with length 1/2 m, width 1/4 m, and height 5/4 m to show that the product is the same as the volume found by packing the prism with 10 unit cubes with an edge length of 1/4 m. What is the volume of the prism?
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